Hexagonal Systems with Minimal Number of Inlets

Let HSh denote the set of hexagonal systems with h hexagons. If U ∈ HSh then the number of inlets of U is denoted by r(U). In this paper we show that r(U) ≥ 3(h − 1) for every U ∈ HSh. Moreover, for every h ≥ 4 we construct hexagonal systems Bh ∈ HSh such that r(Bh) = lp 3(h − 1)